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Exponent Laws & Rules

Index laws

  • Multiplication when the base is the same:
    \[a^m \times a^n = a^{m+n}\]
  • Division when the base is the same:
    \[ a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}\]
  • Power of power rule:
    \[ (a^m)^n = a^{m\times n}\]
  • Power of a product rule:
    \[ (ab)^m = a^m \times b^m\]
  • Fractional power notation:
    \[ a^\frac{m}{n} = \sqrt[n]{a^m}\]
  • The zero index:
    \[a^0 = 1\]
  • The negative index:
    \[ a^{-m}= \frac{1}{a^m}\]